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Articles 18961 - 18990 of 27485

Full-Text Articles in Physical Sciences and Mathematics

Risk Matrix Input Data Biases, Eric D. Smith, William T. Siefert, David Drain Dec 2009

Risk Matrix Input Data Biases, Eric D. Smith, William T. Siefert, David Drain

Engineering Management and Systems Engineering Faculty Research & Creative Works

Risk matrices used in industry characterize particular risks in terms of the likelihood of occurrence, and the consequence of the actualized risk. Human cognitive bias research led by Daniel Kahneman and Amos Tversky exposed systematic translations of objective probability and value as judged by human subjects. Applying these translations to the risk matrix allows the formation of statistical hypotheses of risk point placement biases. Industry-generated risk matrix data reveals evidence of biases in the judgment of likelihood and consequence-principally, likelihood centering, a systematic increase in consequence, and a diagonal bias. Statistical analyses are conducted with linear regression, normal distribution fitting, …

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Using Labeled Data To Evaluate Change Detectors In A Multivariate Streaming Environment, Albert Y. Kim, Caren Marzban, Donald B. Percival, Werner Stuetzle Dec 2009

Using Labeled Data To Evaluate Change Detectors In A Multivariate Streaming Environment, Albert Y. Kim, Caren Marzban, Donald B. Percival, Werner Stuetzle

Statistical and Data Sciences: Faculty Publications

We consider the problem of detecting changes in a multivariate data stream. A change detector is defined by a detection algorithm and an alarm threshold. A detection algorithm maps the stream of input vectors into a univariate detection stream. The detector signals a change when the detection stream exceeds the chosen alarm threshold. We consider two aspects of the problem: (1) setting the alarm threshold and (2) measuring/comparing the performance of detection algorithms. We assume we are given a segment of the stream where changes of interest are marked. We present evidence that, without such marked training data, it might …

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Regularity Of Non-Characteristic Minimal Graphs In The Heisenberg Group ℍ1, Luca Capogna, Giovanna Citti, Maria Manfredini Dec 2009

Regularity Of Non-Characteristic Minimal Graphs In The Heisenberg Group ℍ1, Luca Capogna, Giovanna Citti, Maria Manfredini

Mathematics Sciences: Faculty Publications

Minimal surfaces in the sub-Riemannian Heisenberg group can be constructed by means of a Riemannian approximation scheme, as limit of Riemannian minimal surfaces. We study the regularity of Lipschitz, non-characteristic minimal surfaces which arise as such limits. Our main results are apriori estimates on the solutions of the approximating Riemannian PDE and the ensuing C∞ regularity of the sub-Riemannian minimal surface along its Legendrian foliation.

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Approximating Stationary Statistical Properties, Xiaoming Wang Dec 2009

Approximating Stationary Statistical Properties, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

It is well-known that physical laws for large chaotic dynamical systems are revealed statistically. Many times these statistical properties of the system must be approximated numerically. the main contribution of this manuscript is to provide simple and natural criterions on numerical methods (temporal and spatial discretization) that are able to capture the stationary statistical properties of the underlying dissipative chaotic dynamical systems asymptotically. the result on temporal approximation is a recent finding of the author, and the result on spatial approximation is a new one. Applications to the infinite Prandtl number model for convection and the barotropic quasi-geostrophic model are …

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Non-Negative Steady State Solutions To An Elliptic Biological Model, Brian Ibanez, Joon Hyuk Kang, Jungho Lee Dec 2009

Non-Negative Steady State Solutions To An Elliptic Biological Model, Brian Ibanez, Joon Hyuk Kang, Jungho Lee

Faculty Publications

The non-existence and existence of positive solutions for the generalized predator-prey biological model for two species of animals Δu + ug(u,v) = 0 in Ω, Δv + vh(u,v) = 0 in Ω, u = v = 0 on ∂Ω, is investigated in this paper. The techniques used in this paper are from elliptic theory, the upper-lower solution method, the maximum principles and spectrum estimates. The arguments also rely on detailed properties of solutions to logistic equations. © 2009 Academic Publications.

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A Comparison Theorem For The Topological And Algebraic Classification Of Quaternionic Toric 8-Manifolds, Piotr Runge Dec 2009

A Comparison Theorem For The Topological And Algebraic Classification Of Quaternionic Toric 8-Manifolds, Piotr Runge

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

In order to discuss topological properties of quaternionic toric 8-manifolds, we introduce the notion of an algebraic morphism in the category of toric spaces. We show that the classification of quaternionic toric 8-manifolds with respect to an algebraic isomorphism is finer than the oriented topological classification. We construct infinite families of quaternionic toric 8-manifolds in the same oriented homeomorphism type but algebraically distinct. To prove that the elements within each family are of the same oriented homeomorphism type, and that we have representatives of all such types of a quaternionic toric 8-manifold, we present and use a method of evaluating …

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A Graph Theoretic Summation Of The Cubes Of The First N Integers, Joseph Demaio, Andy Lightcap Dec 2009

A Graph Theoretic Summation Of The Cubes Of The First N Integers, Joseph Demaio, Andy Lightcap

Faculty Articles

In this Math Bite we provide a combinatorial proof of the sum of the cubes of the first n integers by counting edges in complete bipartite graphs.

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A Construction Of Lagrangian Submanifolds In Complex Euclidean Spaces With Legendre Curves, Yun Myung Oh Dec 2009

A Construction Of Lagrangian Submanifolds In Complex Euclidean Spaces With Legendre Curves, Yun Myung Oh

Faculty Publications

In [1], B. Y. Chen provided a new method to construct Lagrangian surfaces in C2 by using Legendre curves in S3(1)C2. In this paper, we investigate the similar methods to construct some Lagrangian submanifolds in complex Euclidean spaces Cn (n≥b3).

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Geometry Of Control-Affine Systems, Jeanne N. Clelland, Christopher G. Moseley, George R. Wilkens Dec 2009

Geometry Of Control-Affine Systems, Jeanne N. Clelland, Christopher G. Moseley, George R. Wilkens

University Faculty Publications and Creative Works

Motivated by control-affine systems in optimal control theory, we introduce the notion of a point-affine distribution on a manifold X - i.e., an affine distribution F together with a distinguished vector field contained in F. We compute local invariants for point-affine distributions of constant type when dim(X) = n, rank(F) = n - 1, and when dim(X) = 3, rank(F) = 1. Unlike linear distributions, which are characterized by integer- valued invariants - namely, the rank and growth vector - when dim(X) ≤ 4, we find local invariants depending on arbitrary functions even for rank 1 point-affine distributions on manifolds …

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Intersection Numbers, Embedded Spheres And Geosphere Laminations For Free Groups., Suhas Pandit Dr. Nov 2009

Intersection Numbers, Embedded Spheres And Geosphere Laminations For Free Groups., Suhas Pandit Dr.

Doctoral Theses

Topological and geometric methods have played a major role in the study of infinite groups since the time of Poincar´e and Klein, with the work of Nielsen, Dehn, Stallings and Gromov showing particularly deep connections with the topology of surfaces and three-manifolds. This is in part because a surface or a 3-manifold is essentially determined by its fundamental group, and has a geometric structure due to the Poincar´e-K¨obe-Klein uniformisation theorem for surfaces and Thurston’s geometrisation conjecture, which is now a theorem of Perelman, for 3-manifolds.A particularly fruitful instance of such an interplay is the relation between intersection numbers of simple …

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Presentations Of Rings With Non-Trivial Semidualizing Modules, David A. Jorgensen, Graham J. Leuschke, Sean Sather-Wagstaff Nov 2009

Presentations Of Rings With Non-Trivial Semidualizing Modules, David A. Jorgensen, Graham J. Leuschke, Sean Sather-Wagstaff

Mathematics - All Scholarship

Let R be a commutative noetherian local ring. A finitely generated R-module C is semidualizing if it is self-orthogonal and satisfies the condition HomR(C,C) \cong R. We prove that a Cohen-Macaulay ring R with dualizing module D admits a semidualizing module C satisfying R\ncong C \ncong D if and only if it is a homomorphic image of a Gorenstein ring in which the defining ideal decomposes in a cohomologically independent way. This expands on a well-known result of Foxby, Reiten and Sharp saying that R admits a dualizing module if and only if R is Cohen-Macaulay and a …

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Hokua – A Wavelet Method For Audio Fingerprinting, Steven S. Lutz Nov 2009

Hokua – A Wavelet Method For Audio Fingerprinting, Steven S. Lutz

Theses and Dissertations

In recent years, multimedia identification has become important as the volume of digital media has dramatically increased. With music files, one method of identification is audio fingerprinting. The underlying method for most algorithms is the Fourier transform. However, due to a lack of temporal resolution, these algorithms rely on the short-time Fourier transform. We propose an audio fingerprinting algorithm that uses a wavelet transform, which has good temporal resolution. In this thesis, we examine the basics of certain topics that are needed in understanding audio fingerprinting techniques. We also look at a brief history of work done in this field. …

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Multiboard Determinacy, Andrés E. Caicedo Nov 2009

Multiboard Determinacy, Andrés E. Caicedo

Andrés E. Caicedo

No abstract provided.

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Comparing Cognitive Decision Models Of Iowa Gambling Task In Indivituals Following Temporal Lobectomy, Jenny Vennukkah Jeyarajah Nov 2009

Comparing Cognitive Decision Models Of Iowa Gambling Task In Indivituals Following Temporal Lobectomy, Jenny Vennukkah Jeyarajah

Mathematics Theses

This study examined the theoretical basis for decision making behavior of patients with right or left temporal lobectomy and a control group when they participated in the Iowa Gambling Task. Two cognitive decision models, Expectancy Valence Model and Strategy Switching Heuristic Choice Model, were compared for best fit. The best fitting model was then chosen to provide the basis for parameter estimation (sources of decision making, i.e. cognitive, motivational, and response processes) and interpretation. Both models outperformed the baseline model. However comparison of G2 means between the two cognitive decision models showed the expectancy valence model having a higher mean …

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Growth And Geodesics Of Thompson's Group F, Jennifer L. Schofield Nov 2009

Growth And Geodesics Of Thompson's Group F, Jennifer L. Schofield

Theses and Dissertations

In this paper our goal is to describe how to find the growth of Thompson's group F with generators a and b. Also, by studying elements through pipe systems, we describe how adding a third generator c affects geodesic length. We model the growth of Thompson's group F by producing a grammar for reduced pairs of trees based on Blake Fordham's tree structure. Then we change this grammar into a system of equations that describes the growth of Thompson's group F and simplify. To complete our second goal, we present and discuss a computer program that has led to some …

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Random Graphs: From Paul Erdős To The Internet, Michał Karoński Nov 2009

Random Graphs: From Paul Erdős To The Internet, Michał Karoński

Dalrymple Lecture Series

Paul Erdős, one of the greatest mathematicians of the twentieth century, was a champion of applications of probabilistic methods in many areas of mathematics, such as a graph theory, combinatorics and number theory. He also, almost fifty years ago, jointly with another great Hungarian mathematician Alfred Rényi, laid out foundation of the theory of random graphs: the theory which studies how large and complex systems evolve when randomness of the relations between their elements is incurred. In my talk I will sketch the long journey of this theory from the pioneering Erdős era to modern attempts to model properties of …

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Counting Pattern-Avoiding Permutations, Lara Pudwell Nov 2009

Counting Pattern-Avoiding Permutations, Lara Pudwell

Lara K. Pudwell

No abstract provided.

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An Introduction To Enumeration Schemes, Lara Pudwell Nov 2009

An Introduction To Enumeration Schemes, Lara Pudwell

Lara K. Pudwell

No abstract provided.

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Homological Dimensions And Regular Rings, Alina Iacob, Srikanth B. Iyengar Nov 2009

Homological Dimensions And Regular Rings, Alina Iacob, Srikanth B. Iyengar

Alina Iacob

A question of Avramov and Foxby concerning injective dimension of complexes is settled in the affirmative for the class of noetherian rings. A key step in the proof is to recast the problem on hand into one about the homotopy category of complexes of injective modules. Analogous results for flat dimension and projective dimension are also established.

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Homological Dimensions And Regular Rings, Alina Iacob, Srikanth B. Iyengar Nov 2009

Homological Dimensions And Regular Rings, Alina Iacob, Srikanth B. Iyengar

Department of Mathematical Sciences Faculty Publications

A question of Avramov and Foxby concerning injective dimension of complexes is settled in the affirmative for the class of noetherian rings. A key step in the proof is to recast the problem on hand into one about the homotopy category of complexes of injective modules. Analogous results for flat dimension and projective dimension are also established.

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Non-Commutative Desingularization Of Determinantal Varieties, I, Ragnar-Olaf Buchweitz, Graham J. Leuschke, Michel Van Den Bergh Nov 2009

Non-Commutative Desingularization Of Determinantal Varieties, I, Ragnar-Olaf Buchweitz, Graham J. Leuschke, Michel Van Den Bergh

Mathematics - All Scholarship

We show that determinantal varieties defined by maximal minors of a generic matrix have a non-commutative desingularization, in that we construct a maximal Cohen-Macaulay module over such a variety whose endomorphism ring is Cohen-Macaulay and has finite global dimension. In the case of the determinant of a square matrix, this gives a non-commutative crepant resolution.

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Counting 1324, 4231-Avoiding Permutations, Michael H. Albert, M. D. Atkinson, Vincent Vatter Nov 2009

Counting 1324, 4231-Avoiding Permutations, Michael H. Albert, M. D. Atkinson, Vincent Vatter

Dartmouth Scholarship

A complete structural description and enumeration is found for permutations that avoid both 1324 and 4231.

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Simplify, Cancel, And Other Math Lingo With Multiple Meanings, Lisa Yocco Nov 2009

Simplify, Cancel, And Other Math Lingo With Multiple Meanings, Lisa Yocco

Lisa S. Yocco

No abstract provided.

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Complementary Lidstone Interpolation And Boundary Value Problems, Ravi P. Agarwal, Sandra Pinelas, Patricia J.Y. Wong Nov 2009

Complementary Lidstone Interpolation And Boundary Value Problems, Ravi P. Agarwal, Sandra Pinelas, Patricia J.Y. Wong

Mathematics and System Engineering Faculty Publications

We shall introduce and construct explicitly the complementary Lidstone interpolating polynomial P 2m (t) of degree 2m, which involves interpolating data at the odd-order derivatives. For P 2m (t) we will provide explicit representation of the error function, best possible error inequalities, best possible criterion for the convergence of complementary Lidstone series, and a quadrature formula with best possible error bound. Then, these results will be used to establish existence and uniqueness criteria, and the convergence of Picard's, approximate Picard's, quasilinearization, and approximate quasilinearization iterative methods for the complementary Lidstone boundary value problems which consist of a (2m+1) th order …

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Area Contraction For Harmonic Automorphisms Of The Disk, Ngin-Tee Koh, Leonid V. Kovalev Nov 2009

Area Contraction For Harmonic Automorphisms Of The Disk, Ngin-Tee Koh, Leonid V. Kovalev

Mathematics - All Scholarship

A harmonic self-homeomorphism of a disk does not increase the area of any concentric disk.

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Fusion Algebras & Accidental Trigonometry, Christopher D. Goff Nov 2009

Fusion Algebras & Accidental Trigonometry, Christopher D. Goff

College of the Pacific Faculty Presentations

No abstract provided.

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Population Coding Of Tone Stimuli In Auditory Cortex: Dynamic Rate Vector Analysis, Peter Bartho, Carina Curto, Artur Luczak, Stephan L. Marguet, Kenneth D. Harris Nov 2009

Population Coding Of Tone Stimuli In Auditory Cortex: Dynamic Rate Vector Analysis, Peter Bartho, Carina Curto, Artur Luczak, Stephan L. Marguet, Kenneth D. Harris

Department of Mathematics: Faculty Publications

Neural representations of even temporally unstructured stimuli can show complex temporal dynamics. In many systems, neuronal population codes show “progressive differentiation,” whereby population responses to different stimuli grow further apart during a stimulus presentation. Here we analyzed the response of auditory cortical populations in rats to extended tones. At onset (up to 300 ms), tone responses involved strong excitation of a large number of neurons; during sustained responses (after 500 ms) overall firing rate decreased, but most cells still showed a statistically significant difference in firing rate. Population vector trajectories evoked by different tone frequencies expanded rapidly along an initially …

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New Effect Size Rules Of Thumb, Shlomo S. Sawilowsky Nov 2009

New Effect Size Rules Of Thumb, Shlomo S. Sawilowsky

Theoretical and Behavioral Foundations of Education Faculty Publications

Recommendations to expand Cohen’s (1988) rules of thumb for interpreting effect sizes are given to include very small, very large, and huge effect sizes. The reasons for the expansion, and implications for designing Monte Carlo studies, are discussed.

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Impact Of Rank-Based Normalizing Transformations On The Accuracy Of Test Scores, Shira R. Solomon, Shlomo S. Sawilowsky Nov 2009

Impact Of Rank-Based Normalizing Transformations On The Accuracy Of Test Scores, Shira R. Solomon, Shlomo S. Sawilowsky

Theoretical and Behavioral Foundations of Education Faculty Publications

The purpose of this article is to provide an empirical comparison of rank-based normalization methods for standardized test scores. A series of Monte Carlo simulations were performed to compare the Blom, Tukey, Van der Waerden and Rankit approximations in terms of achieving the T score’s specified mean and standard deviation and unit normal skewness and kurtosis. All four normalization methods were accurate on the mean but were variably inaccurate on the standard deviation. Overall, deviation from the target moments was pronounced for the even moments but slight for the odd moments. Rankit emerged as the most accurate method among all …

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Hybrid Proximal Methods For Equilibrium Problems, Boris S. Mordukhovich, Barbara Panicucci, Mauro Passacantando, Massimo Pappalardo Nov 2009

Hybrid Proximal Methods For Equilibrium Problems, Boris S. Mordukhovich, Barbara Panicucci, Mauro Passacantando, Massimo Pappalardo

Mathematics Research Reports

This paper concerns developing two hybrid proximal point methods (PPMs) for finding a common solution of some optimization-related problems. First we construct an algorithm to solve simultaneously an equilibrium problem and a variational inequality problem, combing the extragradient method for variational inequalities with an approximate PPM for equilibrium problems. Next we develop another algorithm based on an alternate approximate PPM for finding a common solution of two different equilibrium problems. We prove the global convergence of both algorithms under pseudomonotonicity assumptions.

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